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Effective bounds for Faltings’s delta function

Jay JorgensonJürg Kramer — 2014

Annales de la faculté des sciences de Toulouse Mathématiques

In his seminal paper on arithmetic surfaces Faltings introduced a new invariant associated to compact Riemann surfaces X , nowadays called Faltings’s delta function and here denoted by δ Fal ( X ) . For a given compact Riemann surface X of genus g X = g , the invariant δ Fal ( X ) is roughly given as minus the logarithm of the distance with respect to the Weil-Petersson metric of the point in the moduli space g of genus g curves determined by X to its boundary g . In this paper we begin by revisiting a formula derived in [14],...

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